It is expected that a perturbation at a radius \(r_p\)  would propagate inwards and reach the inner radii after a time-lag equal to the viscous time-scale at \(r_p\) . There are a couple of reasons this expectation might not be met. First, the viscous time-scale computed using equation (REF ) is after all an approximation and hence the actual time-lag associated with the perturbation may differ by a factor of few. More importantly, in a cylindrical geometry, one can expect that the time-lag should have a dependence on the time-period (or frequency) of the perturbation. Unlike
planar waves, the speed of cylindrical sound waves depends on its frequency, which has been exploited to explain frequency dependent time-lags in Cygnus X-1 [1]}. The diffusion equation that describe the propagation here should also have this property and we test whether this is the case, by computing the time-lag between the perturbation and its response in the inner disc region.
